# Scaling Laws for Precision

**Authors:** Tanishq Kumar, Zachary Ankner, Benjamin F. Spector, Blake Bordelon, Niklas Muennighoff, Mansheej Paul, Cengiz Pehlevan, Christopher Ré, Aditi Raghunathan  
**arXiv:** [2411.04330](https://arxiv.org/abs/2411.04330)  
**Date:** 2024-11-07  
**Summary page:** https://www.summarizepaper.com/en/paper/2411.04330v1/

## Key points

- Existing scaling laws do not adequately consider the effects of precision on model quality and cost
- The research team introduces "precision-aware" scaling laws for training and inference processes
- Training in lower precision reduces the model's "effective parameter count," enabling prediction of additional loss from low precision training and post-train quantization
- Degradation introduced by post-training quantization increases as models are trained on more data, potentially making additional pretraining data counterproductive
- Training larger models in lower precision may be computationally optimal
- Unifying scaling laws for post and pretraining quantization into a single functional form offers a comprehensive framework for predicting degradation from training and inference in varied precisions
- The study analyzed over 465 pretraining runs and validated on model sizes up to 1.7B parameters trained on up to 26B tokens
- Insights provided help optimize language model performance through informed decisions regarding precision levels during both training and inference stages

## Summary

In their research on "Scaling Laws for Precision," Tanishq Kumar, Zachary Ankner, Benjamin F. Spector, Blake Bordelon, Niklas Muennighoff, Mansheej Paul, Cengiz Pehlevan, Christopher Ré and Aditi Raghunathan address the impact of low precision training and inference on language models. They highlight that existing scaling laws do not adequately consider the effects of precision on model quality and cost. To bridge this gap, the team introduces "precision-aware" scaling laws for both training and inference processes. By proposing that training in lower precision reduces the model's "effective parameter count," they enable prediction of additional loss incurred from training in low precision and post-train quantization. Their findings suggest that as models are trained on more data, the degradation introduced by post-training quantization increases; potentially rendering additional pretraining data counterproductive. Furthermore, their study reveals that training larger models in lower precision may be computationally optimal. By unifying scaling laws for post and pretraining quantization into a single functional form, the researchers offer a comprehensive framework for predicting degradation from training and inference in varied precisions. Through analysis of over 465 pretraining runs and validation on model sizes up to 1.7B parameters trained on up to 26B tokens,Kumar et al. 's work sheds light on the tradeoffs between precision levels,p arameters,and data in language model development.Their research navigates the complexities of studying scaling in precision by balancing universal functional forms with implementation details of quantization methods.In conclusion,this study provides valuable insights into optimizing language model performance through informed decisions regarding precision levels during both training and inference stages.